Fox News co-president Bill Shine, right, leaves a New York...

Fox News co-president Bill Shine, right, leaves a New York restaurant with Rupert Murdoch, second from right, the executive chairman of 21st Century Fox, on Monday, April 24, 2017. Credit: AP / Mark Lennihan

While other influential allies of President Donald Trump dot the Long Island landscape, the name of Bill Shine, a Head of the Harbor resident, has been widely floated for a possible role on the roiling White House communications team.

Raised in Farmingville, Shine is a former co-president at Fox News. He worked there with Anthony Scaramucci, the Port Washington native and now Manhasset resident, who recently served less than two weeks as Trump’s communications director.

For those just tuning in, “The Mooch” became famous for his colorful, profane rant against top White House aides. Shine, 54, is reputed to be more mannerly. He’s also a friend of Sean Hannity, now a Centre Island resident, who grew up in Franklin Square, according to published reports.

On talk radio and on the Fox channel, commentator Hannity defends Trump and criticizes his detractors, including other Republicans.

Shine was a top deputy of the late Roger Ailes, the network’s founder, who died in May. Much has already been published and reported on the separate sex harassment allegations that had led to Ailes’ ouster.

But for all the public controversy, nobody is likely to deny that Fox still packs an important punch in American conservative politics.

That doesn’t mean the ideologies and affinities of Trump’s Long Island supporters should be regarded as monolithic.

In his recorded, quoted diatribe that helped cut short Scaramucci’s tenure, he was making a point about other Trump aides. One was presidential adviser Steve Bannon, who reportedly had opposed Scaramucci’s hiring.

While deriding Bannon as someone seeking personal gratification, Scaramucci told Ryan Lizza of The New Yorker that by comparison, “I’m not trying to build my own brand off the . . . strength of the president. I’m here to serve the country.”

It seems highly unlikely that such Bannon-bashing would have gone over well with the Mercer family of Head of the Harbor, who are supporters of the president and firm allies of Bannon, former head of the pro-Trump Breitbart News.

Robert Mercer, the co-CEO of Renaissance Technologies, and his daughter Rebekah have also been seen as allied with presidential adviser Kellyanne Conway and former national security adviser Lt. Gen. Michael Flynn.

The bottom line: As the internal politics of the Trump administration churn on, one Long Island player or other will likely play a role.

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